Mr. Nelson calls Minerva a “reimagined university.” Sure, there will be majors and semesters. Admission requirements will be “extraordinarily high,” he says, as at the Ivies. Students will live together and attend classes. And one day, an alumni network will grease job and social opportunities.

But Minerva will have no hallowed halls, manicured lawns or campus. No fraternities or sports teams. Students will spend their first year in San Francisco, living together in a residence hall. If they need to borrow books, says Mr. Nelson, the city has a great public library. Who needs a student center with all of the coffee shops around?

Each of the next six semesters students will move, in cohorts of about 150, from one city to another. Residences and high-tech classrooms will be set up in the likes of São Paulo, London or Singapore—details to come. Professors get flexible, short-term contracts, but no tenure. Minerva is for-profit…

In the Nelson dream curriculum, all incoming students take the same four yearlong courses. His common core won’t make students read the Great Books. “We want to teach you how to think,” Mr. Nelson says. A course on “multimodal communications” works on practical writing and debating skills. A “formal systems class” goes over “everything from logic to advanced stats, Big Data, to formal reasoning, to behavioral econ.”

Over the next three years, Minervaites take small, discussion-heavy seminars via video from their various locations.